TSTP Solution File: NUM394+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:29 EDT 2022
% Result : Theorem 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM394+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 10:30:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Theorem
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 tff(ordinal_subset_type, type, (
% 0.21/0.40 ordinal_subset: ( $i * $i ) > $o)).
% 0.21/0.40 tff(tptp_fun_B_14_type, type, (
% 0.21/0.40 tptp_fun_B_14: $i)).
% 0.21/0.40 tff(tptp_fun_A_13_type, type, (
% 0.21/0.40 tptp_fun_A_13: $i)).
% 0.21/0.40 tff(in_type, type, (
% 0.21/0.40 in: ( $i * $i ) > $o)).
% 0.21/0.40 tff(subset_type, type, (
% 0.21/0.40 subset: ( $i * $i ) > $o)).
% 0.21/0.40 tff(epsilon_transitive_type, type, (
% 0.21/0.40 epsilon_transitive: $i > $o)).
% 0.21/0.40 tff(tptp_fun_B_0_type, type, (
% 0.21/0.40 tptp_fun_B_0: $i > $i)).
% 0.21/0.40 tff(epsilon_connected_type, type, (
% 0.21/0.40 epsilon_connected: $i > $o)).
% 0.21/0.40 tff(ordinal_type, type, (
% 0.21/0.40 ordinal: $i > $o)).
% 0.21/0.40 tff(tptp_fun_A_3_type, type, (
% 0.21/0.40 tptp_fun_A_3: $i)).
% 0.21/0.40 tff(1,plain,
% 0.21/0.40 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(2,plain,
% 0.21/0.40 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.40 tff(3,plain,
% 0.21/0.40 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(4,plain,
% 0.21/0.40 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.40 tff(5,plain,
% 0.21/0.40 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.21/0.40 tff(6,plain,
% 0.21/0.40 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(7,plain,
% 0.21/0.40 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.41 tff(11,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.41 tff(14,plain,(
% 0.21/0.41 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.21/0.41 tff(16,plain,
% 0.21/0.41 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (~((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~(epsilon_transitive(B!14) | (~((~in(tptp_fun_B_0(B!14), B!14)) | subset(tptp_fun_B_0(B!14), B!14)))))) | ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (((~(~ordinal(A!13))) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14))))) <=> (ordinal(A!13) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (ordinal_subset(A, B) | in(B, A))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(24,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (ordinal_subset(A, B) | in(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_ordinal1')).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | ordinal_subset(A, B) | (~ordinal(B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (ordinal(A!13) & (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (~(in(B!14, A!13) | ordinal_subset(A!13, B!14) | (~ordinal(B!14)))),
% 0.21/0.41 inference(and_elim,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (ordinal(B!14)),
% 0.21/0.41 inference(or_elim,[status(thm)],[33])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.41 tff(42,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.41 tff(45,plain,(
% 0.21/0.41 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[44])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!14)) | (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (~((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[50, 47, 34])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (((~epsilon_transitive(B!14)) | (~epsilon_connected(B!14))) | epsilon_transitive(B!14)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (epsilon_transitive(B!14)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | (~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 ((~((~epsilon_transitive(B!14)) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14)))) | ![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (![B: $i] : ((~in(B, B!14)) | subset(B, B!14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 20])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (ordinal(A!13)),
% 0.21/0.41 inference(and_elim,[status(thm)],[32])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.41 tff(62,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(64,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.41 tff(65,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.41 tff(68,plain,(
% 0.21/0.41 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13))) <=> ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)) | (~ordinal(B!14)) | (~ordinal(A!13)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(B!14)) | (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (ordinal_subset(A!13, B!14) <=> subset(A!13, B!14)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[76, 70, 57, 34])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (~ordinal_subset(A!13, B!14)),
% 0.21/0.41 inference(or_elim,[status(thm)],[33])).
% 0.21/0.41 tff(79,plain,
% 0.21/0.41 ((~(ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))) | ordinal_subset(A!13, B!14) | (~subset(A!13, B!14))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(80,plain,
% 0.21/0.41 ((~(ordinal_subset(A!13, B!14) <=> subset(A!13, B!14))) | (~subset(A!13, B!14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.41 tff(81,plain,
% 0.21/0.41 (~subset(A!13, B!14)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))) <=> ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | ((~in(A!13, B!14)) | subset(A!13, B!14))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 ((~![B: $i] : ((~in(B, B!14)) | subset(B, B!14))) | (~in(A!13, B!14)) | subset(A!13, B!14)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (~in(A!13, B!14)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[84, 81, 56])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[89, 87])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.42 tff(96,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.21/0.42 tff(99,plain,(
% 0.21/0.42 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[98])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B)))) <=> ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[104, 102])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[107, 101, 34])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (~in(B!14, A!13)),
% 0.21/0.42 inference(or_elim,[status(thm)],[33])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(111,plain,
% 0.21/0.42 (((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13)) <=> ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[111])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13))),
% 0.21/0.42 inference(transitivity,[status(thm)],[112, 110])).
% 0.21/0.42 tff(114,plain,
% 0.21/0.42 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(A!13)) | in(A!13, B!14) | in(B!14, A!13) | (B!14 = A!13))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(A!13)) | in(B!14, A!13) | in(A!13, B!14) | (B!14 = A!13)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (in(A!13, B!14) | (B!14 = A!13)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[115, 57, 109, 108])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (B!14 = A!13),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[116, 85])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (ordinal_subset(A!13, B!14) <=> ordinal_subset(A!13, A!13)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (ordinal_subset(A!13, A!13) <=> ordinal_subset(A!13, B!14)),
% 0.21/0.42 inference(symmetry,[status(thm)],[118])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl((ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)))), rewrite((((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(123,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.42 tff(124,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(125,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(126,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.42 tff(127,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_ordinal1')).
% 0.21/0.42 tff(128,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.21/0.43 tff(130,plain,(
% 0.21/0.43 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 0.21/0.43 inference(skolemize,[status(sab)],[129])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A)) <=> ?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (^[A: $i] : rewrite(((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)) <=> (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (?[A: $i] : ((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)) <=> ?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.43 tff(136,axiom,(?[A: $i] : ((epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_ordinal1')).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (?[A: $i] : (epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.21/0.43 tff(139,plain,(
% 0.21/0.43 epsilon_transitive(A!3) & epsilon_connected(A!3) & ordinal(A!3)),
% 0.21/0.43 inference(skolemize,[status(sab)],[138])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (ordinal(A!3)),
% 0.21/0.43 inference(and_elim,[status(thm)],[139])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13))) <=> ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[142])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13))),
% 0.21/0.43 inference(transitivity,[status(thm)],[143, 141])).
% 0.21/0.43 tff(145,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(A!13, A!13) | (~ordinal(A!3)) | (~ordinal(A!13)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!13)) | (~ordinal(A!3)) | ordinal_subset(A!13, A!13)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (ordinal_subset(A!13, A!13)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[146, 140, 132, 57])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (ordinal_subset(A!13, B!14)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[147, 119])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[78, 148])).
% 0.21/0.43 % SZS output end Proof
%------------------------------------------------------------------------------